Free Energy on a Cycle Graph and Trigonometric Deformation of Heat Kernel Traces on Odd Spheres

TL;DR

This paper explores a trigonometric deformation of heat kernel traces on odd spheres, inspired by discretized circle models, and computes the associated free energies using Bessel function expansions.

Contribution

It introduces a novel deformation approach for heat kernel traces on odd spheres and calculates free energies through Bessel function expansions, extending previous geometric analysis.

Findings

Derived deformed heat kernel trace expressions

Computed free energies for the deformed models

Established regularization methods for the calculations

Abstract

We consider a possible `deformation' of the trace of the heat kernel on odd dimensional spheres, motivated by the calculation of the free energy of a scalar field on a discretized circle. By using an expansion in terms of the modified Bessel functions, we obtain the values of the free energies after a suitable regularization.